At a Fox News Town Hall with Chris Wallace on Sunday in downtown Des Moines, Iowa, Pete Buttigieg joined a chorus of Democrats in calling for former national security adviser John Bolton to testify, following reports that he directly linked President Trump's hold on Ukraine aid to his push for investigations of Joe and Hunter Biden.

Trump told Bolton in August, according to a transcript of Bolton's forthcoming book reviewed by The New York Times, “that he wanted to continue freezing $391 million in security assistance to Ukraine until officials there helped with investigations into Democrats including the Bidens."

Late Sunday, a senior advisor to Bolton, speaking to Fox News, denied the Times' reporting that Bolton had shared any portion of his manuscript with "close associates." The advisor said Bolton had only shared the book with national security officials as part of a standard classification review process, and would not speculate as to how the Times may have come across an early version of the book.

"Just now, we're getting more indications about John Bolton, and what he knew, which is one more reason why, if this is a serious trial, we're going to have the witnesses and evidence," Buttigieg said.

And, responding to reports that a dining hall at the U.S. Embassy in Baghdad had just come under attack, Buttigieg insisted on steps to ensure a "proportional response or preventative actions to make sure that this can't happen again." A senior U.S. defense official initially described it as a rocket attack, but sources told Fox News on Monday the attack involved 60-mm mortars.

He then slammed Trump for supposedly "faking an injury" to avoid serving in Vietnam, and said it was "disturbing" that Trump had minimized the apparent injuries to U.S. troops in a previous Iranian-backed attack on U.S. bases in Iraq. The Pentagon initially said the Iran attack had caused no injuries, before later reevaluating and finding that 34 soldiers had concussions; Trump characterized the injuries as "headaches" and "not very serious."

The Town Hall, which was taking place with just days to go until the do-or-die, first-in-the-nation caucuses are held in Iowa on Feb. 3, afforded Buttigieg the opportunity to respond to a series of breaking-news events. He began the town hall by offering condolences for the death of NBA star Kobe Bryant.

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Meanwhile, Trump's lawyers this week are set to resume presenting their defense in the Senate, which will then decide whether to hear additional witnesses by a simple majority vote. At the Town Hall, Buttigieg emphasized that Trump should be removed from office -- a highly unlikely eventuality, given that a two-thirds vote of the GOP-controlled Senate would be necessary.

Pete Buttigieg speaking at the University of Dubuque in Dubuque, Iowa, this past Wednesday. (AP Photo/Gene J. Puskar)

Separately, as he acknowledged that the economy was doing well by most metrics, Buttigieg defended his demand for more than $5 trillion in new spending on health care and child care as "the right thing to do." Additionally, Buttigieg claimed his proposals were "deficit-neutral" at worst.

"One thing we can do, is deliver a quality public plan where the premiums never go about 8.5 percent of your income," Buttigieg said. "We also need to make sure that we're prepared to fund the subsidies that make health care affordable. ... And that means we can't be afraid to talk about revenue."

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Buttigieg called for two changes: a repeal of Trump's tax cuts, which slashed both the corporate and individual tax rates, and "finally [allowing] Medicare to negotiate the price of prescription drugs with the drug companies."

On climate change, Buttigieg said he's not "going to be dogmatic" like many progressives in their opposition to nuclear energy, and that he thought it was a valid solution in the "short term" and "medium term." But, he said there were "too many questions" about potential effects of nuclear energy in the "long term."

Just days after Trump became the first president ever to appear at the March for Life pro-life rally, Buttigieg also fielded a question from Kristen Day, the president of the organization Democrats for Life -- and the conversation quickly became tense.

"I'm a proud pro-life Democrat. So, do you want the support of pro-life Democrats?" Day asked. "And if so, would you support more moderate platform language in the Democratic Party to ensure the party of diversity and inclusion really does include everybody?"

Buttigieg responded: "I'm not going to try to earn your vote by tricking you. I am pro-choice, and I believe that a woman ought to be able to make that decision. But I know that the difference of opinion that you and I have is one that we have come by honestly. And the best that I can offer, and it may win your vote, and if not, I understand. The best that I can offer is that, if we can't agree on where to draw the line, the next best thing we can do is agree on who should draw the line. And in my view, it's the woman who is faced with that decision in her own life."

Then, Wallace asked if Day was satisfied by Buttigieg's response -- and Day was unequivocal.

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"I was not, because he didn't answer the second part of my question," Day said. "The Democratic platform contains language that basically says that we don't belong, we have no part in the party because it says abortion should be legal up to nine months; the government should pay for it. And there's nothing that says that people that have a diversity of views on this issue should be included in the party."

Buttigieg emphasized that he had "never encountered a politician or frankly another person that I agreed with 100% of the time, even on very important things."

"I support the position of my party that this kind of medical care needs to be available to everyone," Buttigieg continued. "And I support the Roe v. Wade framework that holds that early in pregnancy, there are very few restrictions and later in pregnancy, there are very few exceptions. And again, the best I can offer is that we may disagree on that very important issue, and hopefully we'll be able to partner on other issues. ... I cannot imagine that a decision that a woman confronts is going to ever be better medically or morally because it's being dictated by any government official. And that's just where I am on the issue."

It was the Democrat’s second appearance at a Fox News Town Hall, after he took on President Trump and pitched a series of tax hikes at a New Hampshire event last May. The stakes are higher this time around, as Buttigieg's rising poll numbers in Iowa -- and warning signs in future primary states -- have created both high expectations and little room for error.

"I’m not sure a win is necessary, but he’s got to be in the top two, I would think, to have any chance of moving on,” said Joe Trippi, former Vermont Gov. Howard Dean's 2004 presidential campaign manager.

“He has to beat Biden in Iowa to keep this going in a serious way," remarked David Axelrod, an architect of President Obama's 2008 victory. “The predicate of his race has always been he’s a younger, more contemporary, sturdier alternative to [Joe] Biden in the center-left lane. If Biden does better than him, it kind of destroys the predicate.”

The hyperpartisan nature of the electorate has created its own challenge. In an email to supporters this week, Lis Smith, Buttigieg’s senior communications advisor, offered a lengthy explanation as to why the 38-year-old former South Bend, Ind., mayor was appearing on Fox News. Other candidates, including Sen. Elizabeth Warren, D-Mass., have shunned the network, and the Democratic National Committee (DNC) barred Fox News from hosting one of its presidential primary debates.

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"We can’t play it safe. We can’t afford to write off voters," Smith's email read. "Pete broke through with his CNN town hall last March, and even had Donald Trump attacking him after his Fox News town hall dominated the national conversation."

This weekend, fellow presidential candidate Andrew Yang backed up that approach in Iowa. “One thing I think Democrats should do, I think we should go on Fox News and talk to the American people,” Yang said. “How can you win an election and bring the country together if you literally won’t talk to 40 or 50 percent of the population?”

Yang added: “This is something I’d say that is critical of the DNC. There was a decision early on in the process where Fox News said, ‘We’d like to host a DNC debate.’ And, to me, if you’re the DNC, you jump at that. You’re like, ‘Let me show my candidates to people who generally watch Fox News.’ But, the DNC turned it down! I was like, ‘What are you doing?’”

Iowa has posed unique opportunities, and possible pitfalls, for Buttigieg’s campaign. A New York Times/Siena College survey showed Sen. Bernie Sanders, I-Vt., ahead of Buttigieg by eight points and Biden by nine points -- a narrow gap at second-place that afforded Buttigieg an opportunity to make a splash. Sanders has pulled far ahead in New Hampshire, as well, though, potentially signaling that progressives wanted more radical change than Buttigieg has promised.

Additionally, Sanders and Warren could take disappointing Iowa finishes to New Hampshire, where they’ve had regional followings, and try, in effect, to cancel out the first contest quickly. Sanders and Warren also had more online donors -- Warren less so -- who could sustain them through any setbacks.

Buttigieg has polled very low among African American voters, who are expected to make up roughly two-thirds of the electorate in the South Carolina primary.

However, Buttigieg is also doing fairly well in New Hampshire, and campaign aides said a top finish in Iowa could slingshot Buttigieg and would lead to a competitive New Hampshire.

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While the half dozen strategists who have advised top-tier Democrats in Iowa said Buttigieg didn’t have to win, several said finishing behind Biden would be trouble.

“If Buttigieg can beat Biden, and [Amy] Klobuchar, it sets him up to be a real alternative to Sanders and Warren,” the two most progressive candidates in the top tier, said Jennifer Psaki, an Obama campaign alum who served in the White House and State Department. “That’s key for him moving forward.”

Fox News' Paul Steinhauser in Des Moines, Iowa, and The Associated Press contributed to this report.